Two points `P and Q` in a plane are related if `OP = OQ,` where is a fixed point. This relation is :

Let O be the origin.We define a relation between two points P and Q in a plane if OP=OQ. Show that the relation,so defined is an equivalence relation.

Let O be the origin.We define a relation between two points P and Q in a plane if OP=OQ. Show that the relation,so defined is an equivalence relation.

In the figure, angleQPR = anglePQR and M and N are respectively on sides QR and PR such that QM = PN. Prove that OP=OQ, where O is the point of intersection of PM and QN.

A point moves in a plane so that its distances PA and PB from two fixed points A and B in the plane satisfy the relation PA-PB=k(k ne 0) , then the locus of P , is

Let z_(1) and z_(2) be the roots of the equation z^(2)+pz+q=0 . Suppose z_(1) and z_(2) are represented by points A and B in the Argand plane such that angleAOB=alpha , where O is the origin. Statement-1: If OA=OB, then p^(2)=4q cos^(2)alpha/2 Statement-2: If affix of a point P in the Argand plane is z, then ze^(ia) is represented by a point Q such that anglePOQ =alpha and OP=OQ .

Let P(-7,1,-5) be a point on a plane and let O be the origin. If OP is normal to the plane, then the equation of the plane is